# Are these trigonometric functions even or odd?

• October 6th 2011, 02:08 PM
essedra
Are these trigonometric functions even or odd?
x(t) = 20cos(2π*40t-0.4π)

x(t) = exp(-8πt)

x[n] = exp(cos(2πn/5))

x[n] = u[n] + u[-n]

x[n] = u[n] - u[-n] + 5δ[n]

• October 6th 2011, 02:27 PM
skeeter
Re: Are these trigonometric functions even or odd?
Quote:

Originally Posted by essedra
x(t) = 20cos(2π*40t-0.4π)

x(t) = exp(-8πt)

x[n] = exp(cos(2πn/5))

x[n] = u[n] + u[-n]

x[n] = u[n] - u[-n] + 5δ[n]

f(-x) = f(x) ... even

f(-x) = -f(x) ... odd

now what?
• October 6th 2011, 03:02 PM
essedra
Re: Are these trigonometric functions even or odd?
Quote:

Originally Posted by skeeter
f(-x) = f(x) ... even

f(-x) = -f(x) ... odd

now what?

Yes, I know, but how can I apply this and see the result?

I mean to decompose them into even & odd parts?
• October 6th 2011, 03:18 PM
skeeter
Re: Are these trigonometric functions even or odd?
Quote:

x(t) = 20cos(2π*40t-0.4π)
$x(t) = 20\cos(80\pi t - 0.4\pi)$

$x(-t) = 20 \cos(-80\pi t - 0.4\pi) = 20\cos[-(80\pi t + 0.4\pi)] = 20 \cos(80\pi t + 0.4\pi)$

final result ... x(-t) is not equal to x(t) or -x(t) ... x(t) is neither even or odd
• October 6th 2011, 03:19 PM
Plato
Re: Are these trigonometric functions even or odd?
Quote:

Originally Posted by essedra
Yes, I know, but how can I apply this and see the result?

Sometimes one must just have some prior information.
The function $\cos(x)$ is even and $\sin(x)$ is odd.
On the other hand, you should be able to prove that $f(x)=|x|$ is even.

Can you show that $f(x)=e^x$ is neither even nor odd?
• October 6th 2011, 03:26 PM
essedra
Re: Are these trigonometric functions even or odd?
Quote:

Originally Posted by Plato
Sometimes one must just have some prior information.
The function $\cos(x)$ is even and $\sin(x)$ is odd.
On the other hand, you should be able to prove that $f(x)=|x|$ is even.

Can you show that $f(x)=e^x$ is neither even nor odd?

I can interprete it from the graph of the function, that it's not even nor odd, but I don't know how to prove it...
• October 6th 2011, 03:33 PM
Plato
Re: Are these trigonometric functions even or odd?
Quote:

Originally Posted by essedra
I can interprete it from the graph of the function, that it's not even nor odd, but I don't know how to prove it...

For all $x$:

Is is possible that $e^x=e^{-x}~?$

Is is possible that $-e^x=e^{-x}~?$

If the answer to both is no, then it is neither even nor odd.
• October 6th 2011, 03:35 PM
essedra
Re: Are these trigonometric functions even or odd?
Oh, I see now. It's simple as cake. Thank you...